| Characteristic | Overall N = 1801 |
ABC N = 301 |
ACB N = 301 |
BAC N = 301 |
BCA N = 301 |
CAB N = 301 |
CBA N = 301 |
p-value2 |
|---|---|---|---|---|---|---|---|---|
| Age (years) | 32 (8) [18, 45] | 33 (8) [19, 44] | 31 (7) [18, 42] | 31 (7) [20, 44] | 33 (8) [19, 45] | 32 (7) [21, 44] | 31 (7) [20, 44] | 0.6 |
| Race | 0.9 | |||||||
| Â Â Â Â Black | 64 (36%) | 12 (40%) | 13 (43%) | 12 (40%) | 10 (33%) | 8 (27%) | 9 (30%) | |
| Â Â Â Â White | 52 (29%) | 8 (27%) | 9 (30%) | 7 (23%) | 7 (23%) | 12 (40%) | 9 (30%) | |
| Â Â Â Â Other | 64 (36%) | 10 (33%) | 8 (27%) | 11 (37%) | 13 (43%) | 10 (33%) | 12 (40%) | |
| Female | 81 (45%) | 13 (43%) | 11 (37%) | 16 (53%) | 14 (47%) | 12 (40%) | 15 (50%) | 0.8 |
| 1 Mean (SD) [Min, Max]; n (%) | ||||||||
| 2 Kruskal-Wallis rank sum test; Pearson’s Chi-squared test | ||||||||
No apparent difference in starting value by period or treatment, so looking at change from baseline in PK
Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit
Notation: \(k =\) subject, \(i =\) treatment, \(j =\) period,
\[ \begin{align} Y_{ijk} &= \mu + b_{ik} + \tau_{ij} + \varepsilon_{ijk},\\ b_{ik} &\sim N(0, \sigma_k^2), \\ \varepsilon_{ij} &\sim N(0, \sigma^2), \end{align} \]
Findings: Significantly less decrease in gels vs pill A
## Data: merged
## Models:
## model: bloodVL_change ~ treatment + period + (1 | ptid)
## model_large: bloodVL_change ~ treatment + sequence_ind + period + (1 | ptid)
## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)
## model 7 4926.1 4956.1 -2456.0 4912.1
## model_large 8 4927.2 4961.5 -2455.6 4911.2 0.8686 1 0.3513
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bloodVL_change ~ treatment + period + (1 | ptid)
## Data: merged
##
## REML criterion at convergence: 4896.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7874 -0.6001 0.0430 0.6241 2.4126
##
## Random effects:
## Groups Name Variance Std.Dev.
## ptid (Intercept) 41.2 6.419
## Residual 489.2 22.117
## Number of obs: 540, groups: ptid, 180
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 122.243 2.181 513.694 56.040 < 0.0000000000000002 ***
## treatmentGel B -10.889 2.331 356.000 -4.671 0.000004264 ***
## treatmentGel C -11.656 2.331 356.000 -4.999 0.000000904 ***
## periodperiod2 -1.533 2.331 356.000 -0.658 0.511
## periodperiod3 -1.711 2.331 356.000 -0.734 0.463
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trtmGB trtmGC prdpr2
## treatmntGlB -0.534
## treatmntGlC -0.534 0.500
## periodperd2 -0.534 0.000 0.000
## periodperd3 -0.534 0.000 0.000 0.500
| Characteristic | Beta | 95% CI | p-value |
|---|---|---|---|
| treatment | |||
|     Pill A | — | — | |
| Â Â Â Â Gel B | -11 | -15, -6.3 | <0.001 |
| Â Â Â Â Gel C | -12 | -16, -7.1 | <0.001 |
| period | |||
|     period1 | — | — | |
| Â Â Â Â period2 | -1.5 | -6.1, 3.1 | 0.5 |
| Â Â Â Â period3 | -1.7 | -6.3, 2.9 | 0.5 |
| Abbreviation: CI = Confidence Interval | |||
Findings: Significantly less decrease in gels vs pill A
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: skinVL_change ~ treatment + sequence_ind + period + (1 | ptid)
## Data: merged
##
## REML criterion at convergence: 5390.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4199 -0.5952 0.0426 0.7273 3.2412
##
## Random effects:
## Groups Name Variance Std.Dev.
## ptid (Intercept) 0 0.00
## Residual 1339 36.59
## Number of obs: 540, groups: ptid, 180
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 205.2176 4.0145 534.0000 51.119 < 0.0000000000000002 ***
## treatmentGel B -32.4056 3.8570 534.0000 -8.402 0.0000000000000004 ***
## treatmentGel C -41.9222 3.8570 534.0000 -10.869 < 0.0000000000000002 ***
## sequence_ind -0.9472 1.9285 534.0000 -0.491 0.624
## periodperiod2 2.5000 3.8570 534.0000 0.648 0.517
## periodperiod3 1.2722 3.8570 534.0000 0.330 0.742
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trtmGB trtmGC sqnc_n prdpr2
## treatmntGlB -0.480
## treatmntGlC -0.480 0.500
## sequence_nd -0.480 0.000 0.000
## periodperd2 -0.480 0.000 0.000 0.000
## periodperd3 -0.480 0.000 0.000 0.000 0.500
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
## Data: merged
## Models:
## model: skinVL_change ~ treatment + period + (1 | ptid)
## model_large: skinVL_change ~ treatment + sequence_ind + period + (1 | ptid)
## npar AIC BIC logLik -2*log(L) Chisq Df Pr(>Chisq)
## model 7 5428.4 5458.5 -2707.2 5414.4
## model_large 8 5430.2 5464.5 -2707.1 5414.2 0.2439 1 0.6214
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: skinVL_change ~ treatment + period + (1 | ptid)
## Data: merged
##
## REML criterion at convergence: 5394.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4223 -0.5960 0.0491 0.7339 3.2176
##
## Random effects:
## Groups Name Variance Std.Dev.
## ptid (Intercept) 0.0000000000000001573 0.00000001254
## Residual 1336.9992661820692774199 36.56500056314
## Number of obs: 540, groups: ptid, 180
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 204.270 3.518 535.000 58.057 < 0.0000000000000002 ***
## treatmentGel B -32.406 3.854 535.000 -8.408 0.000000000000000381 ***
## treatmentGel C -41.922 3.854 535.000 -10.877 < 0.0000000000000002 ***
## periodperiod2 2.500 3.854 535.000 0.649 0.517
## periodperiod3 1.272 3.854 535.000 0.330 0.741
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trtmGB trtmGC prdpr2
## treatmntGlB -0.548
## treatmntGlC -0.548 0.500
## periodperd2 -0.548 0.000 0.000
## periodperd3 -0.548 0.000 0.000 0.500
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
| Characteristic | Beta | 95% CI | p-value |
|---|---|---|---|
| treatment | |||
|     Pill A | — | — | |
| Â Â Â Â Gel B | -32 | -40, -25 | <0.001 |
| Â Â Â Â Gel C | -42 | -49, -34 | <0.001 |
| period | |||
|     period1 | — | — | |
| Â Â Â Â period2 | 2.5 | -5.1, 10 | 0.5 |
| Â Â Â Â period3 | 1.3 | -6.3, 8.8 | 0.7 |
| Abbreviation: CI = Confidence Interval | |||
| Characteristic | Beta | SE | 95% CI | p-value |
|---|---|---|---|---|
| treatment | ||||
|     Pill A | — | — | — | |
| Â Â Â Â Gel B | -32 | 3.85 | -40, -25 | <0.001 |
| Â Â Â Â Gel C | -42 | 3.85 | -49, -34 | <0.001 |
| period | ||||
|     period1 | — | — | — | |
| Â Â Â Â period2 | 2.5 | 3.85 | -5.1, 10 | 0.5 |
| Â Â Â Â period3 | 1.3 | 3.85 | -6.3, 8.8 | 0.7 |
| Abbreviations: CI = Confidence Interval, SE = Standard Error | ||||
Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit
Q: include treatment X adherence and treatment X AE interaction terms???
Skin/Blood PK ~ Random Intercept (Subject) + Treatment + Adherence + Carryover + Period
## Model df AIC BIC logLik Test L.Ratio p-value
## model 1 7 5307.160 5337.201 -2646.580
## model_large 2 10 5312.149 5355.064 -2646.074 1 vs 2 1.011282 0.7985
## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 5307.16 5337.201 -2646.58
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 0.003649564 32.52911
##
## Fixed effects: skinVL_change ~ treatment + overall_adhere + overall_safety
## Value Std.Error DF t-value p-value
## (Intercept) 162.22787 7.582825 356 21.394119 0
## treatmentGel B -24.41464 3.625130 356 -6.734832 0
## treatmentGel C -36.99593 3.543320 356 -10.441036 0
## overall_adhere 1.81506 0.274724 356 6.606870 0
## overall_safety1 -55.77639 5.201704 356 -10.722715 0
## Correlation:
## (Intr) trtmGB trtmGC ovrll_
## treatmentGel B -0.509
## treatmentGel C -0.443 0.534
## overall_adhere -0.945 0.311 0.234
## overall_safety1 0.139 -0.079 -0.032 -0.205
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.43058828 -0.67881147 0.02915247 0.64404884 3.53027310
##
## Number of Observations: 540
## Number of Groups: 180
## Model df AIC BIC logLik Test L.Ratio p-value
## model 1 7 4860.258 4890.299 -2423.129
## model_large2 2 11 4851.039 4898.246 -2414.519 1 vs 2 17.21954 0.0018
## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 4860.258 4890.299 -2423.129
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 4.74164 21.00209
##
## Fixed effects: bloodVL_change ~ treatment + overall_adhere + overall_safety
## Value Std.Error DF t-value p-value
## (Intercept) 98.73209 5.172962 356 19.086184 0.0000
## treatmentGel B -6.81051 2.354117 356 -2.893020 0.0041
## treatmentGel C -9.10003 2.295483 356 -3.964320 0.0001
## overall_adhere 0.93216 0.187884 356 4.961396 0.0000
## overall_safety1 -26.34806 3.460017 356 -7.615009 0.0000
## Correlation:
## (Intr) trtmGB trtmGC ovrll_
## treatmentGel B -0.513
## treatmentGel C -0.443 0.538
## overall_adhere -0.949 0.327 0.247
## overall_safety1 0.131 -0.079 -0.032 -0.195
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.5553528690 -0.5673073777 0.0005900677 0.6043037231 3.0550971969
##
## Number of Observations: 540
## Number of Groups: 180
## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 4851.039 4898.246 -2414.519
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 5.176441 20.56066
##
## Fixed effects: bloodVL_change ~ treatment * overall_adhere + treatment * overall_safety
## Value Std.Error DF t-value p-value
## (Intercept) 131.74236 14.431943 352 9.128525 0.0000
## treatmentGel B -39.19101 15.315595 352 -2.558895 0.0109
## treatmentGel C -52.11513 15.650359 352 -3.329964 0.0010
## overall_adhere -0.36462 0.545375 352 -0.668563 0.5042
## overall_safety1 -11.39117 5.811353 352 -1.960158 0.0508
## treatmentGel B:overall_adhere 1.31391 0.591905 352 2.219795 0.0271
## treatmentGel C:overall_adhere 1.73440 0.603583 352 2.873511 0.0043
## treatmentGel B:overall_safety1 -25.67859 8.049524 352 -3.190076 0.0016
## treatmentGel C:overall_safety1 -17.98165 8.518057 352 -2.111003 0.0355
## Correlation:
## (Intr) trtmGB trtmGC ovrll_ ovrl_1 trGB:_ trGC:_
## treatmentGel B -0.924
## treatmentGel C -0.901 0.841
## overall_adhere -0.993 0.919 0.895
## overall_safety1 0.113 -0.109 -0.107 -0.147
## treatmentGel B:overall_adhere 0.895 -0.986 -0.816 -0.901 0.138
## treatmentGel C:overall_adhere 0.875 -0.818 -0.988 -0.881 0.135 0.804
## treatmentGel B:overall_safety1 -0.080 0.118 0.075 0.104 -0.717 -0.173 -0.096
## treatmentGel C:overall_safety1 -0.075 0.073 0.113 0.098 -0.678 -0.093 -0.160
## tGB:_1
## treatmentGel B
## treatmentGel C
## overall_adhere
## overall_safety1
## treatmentGel B:overall_adhere
## treatmentGel C:overall_adhere
## treatmentGel B:overall_safety1
## treatmentGel C:overall_safety1 0.492
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.63070078 -0.59111860 -0.02603496 0.59219448 2.76927257
##
## Number of Observations: 540
## Number of Groups: 180